A neutron moving with a speed v makes a head on collision with a hydrogen atom in ground state kept at rest. The minimum kinetic energy of neutron for which inelastic collision will take place is

Step-by-step solution

Let v= speed of neutron before collision v₁= speed of neutron after collision v₂= speed of hydrogen atom after collision and E= energy of the excitation From the conservation of linear momentum, m v=m v₁+m v₂ ...(i) From the conservation of energy, 1 2 m v^2= 1 2 m v₁^2+ 1 2 m v₂^2+ E ...(ii) from Eq. (i), v^2=v₁^2+v₂^2+2 v₁ v₂ From Eq. (ii), array rlrl & & v^2 & =v₁^2+v₂^2+ 2 E m & & 2 v₁ v₂ & = 2 E m & & (v₁-v₂ )^2 & = (v₁+v₂ )^2-4 v₁ v₂ & & =v^2- 4 E m array As, v₁-v₂ must be real v^2- 4 E m 0 or 1 2 m v^2 2 E T